Heat oven to 350°F.
Whisk chutney, curry and ginger in saucepan. Boil, stirring, 3 minutes. Cool slightly. Add yogurt. Scrape into bowl. Add turkey. Chill several hours.
Wrap 4 tortillas in aluminum foil. Heat in 350°F oven for 10 minutes.
Coat outside of 4 deep 10-ounce custard cups with cooking spray. Invert cups onto baking sheets. Remove tortillas from oven. Increase oven temperature to 400°F. Place 1 tortilla (keep remaining wrapped in foil) on cup, pressing to shape; repeat with others.
Bake tortillas on cups in 400°F oven 10 minutes. Cool shells on wire rack.
Add papaya, kiwi and almonds to turkey mixture. Line tortilla cups with spinach. Fill with turkey mixture.